Preheat a gas grill on high, covered, for 10 minutes, then turn heat to medium. Pat lamb chops dry with paper towels and sprinkle generously with salt and pepper. Grill, turning once, until cooked to desired doneness, 8 to 10 minutes total for medium-rare. Remove chops from grill, tent with foil and let rest on a cutting board or plate for 5 minutes.

While lamb chops are cooking, toss greens, tomatoes, cucumber, olives, onion, oil and lemon juice in a large bowl. Divide salad among 4 plates. Top each plate with a chop, sprinkle salad with cheese and oregano and serve immediately.